(i) The altitude of a research drone HHH, measured in decameters, is modeled by the function H(t)=e−0.4tsec0.5t,0≤t<πH(t) = \text{e}^{-0.4t} \sec 0.5t, \quad 0 \le t < \piH(t)=e−0.4tsec0.5t,0≤t<π where ttt is the time in minutes after deployment.
Find H′(t)H'(t)H′(t).
Hence determine the time ttt at which the altitude of the drone is stationary.
A separate flight path is defined by the implicit relationship x=ln(2siny),0<y<π2x = \ln(2\sin y), \quad 0 < y < \frac{\pi}{2}x=ln(2siny),0<y<2π Show that dydx=exf(x)\frac{\text{d}y}{\text{d}x} = \frac{\text{e}^x}{\text{f}(x)}dxdy=f(x)ex where f(x)\text{f}(x)f(x) is a function of ex\text{e}^xex that should be found.
Practise Edexcel A Level Maths 9.4 The Product Rule with exam-style questions for A Level Maths. 30 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.